Various types of sheet feeding arrangements are known which use vacuum suction cups or other pick-up devices in which a topmost sheet from a stack is pulled off, supplied to a make-ready table in shingled, staggered overlapping relation where it is properly aligned with respect to a lateral and a front stop and is then supplied to a rotary printing transport apparatus, for example a printing cylinder, a transport drum or the like, by means of a rocking or reciprocating gripper (see, for example, German Published Patent Application DE-AS No. 25 18 220). The sheets are separated from the stack and then transported to the make-ready table by means of suction devices, transport rollers, transport belts and webs or the like. To then supply the partly overlapping sheets requires a gripper which reciprocates between the sheet on the make-ready table and the grippers on the transport device, typically a transport drum which is comparatively complex. The transfer gripper must be twice accelerated and retarded which results in substantial use of energy to overcome inertial forces. With the tendency to increase the speed of rotary printing machines, that is, with a higher through-put of sheets per unit time, the inertial forces of the gripper mechanism become considerable and interfere with operation of the gripper apparatus.